The event Generator. Chris/an Bauer. Lawrence Berkeley Na/onal Laboratory. Theorie Palaver, Mainz April

Transcription

1 The event Generator Chris/an Bauer Lawrence Berkeley Na/onal Laboratory Theorie Palaver, Mainz April The GENEVA Collaboration: Simone Alioli, CWB, Calvin Berggren, Andrew Hornig, Frank Tackmann, Christopher Vermilion, Jonathan Walsh, and Saba Zuberi

2 This talk describes our recent development of a new event generator called GENEVA What are we trying to do An illustra4ve example The GENEVA framework Results for e+e- event shapes Progress towards pp collisions

3 This talk describes our recent development of a new event generator called GENEVA What are we trying to do An illustra4ve example The GENEVA framework Results for e+e- event shapes Progress towards pp collisions

4 An event generator gives the fully differen/al cross sec/on for events that represent real events seen at the LHC Main problem: How do we calculate a cross- sec4on for events containing 100 s of par4cles? How do we calculate a cross- sec4on that is valid in all kinema4cal regions?

5 Theore/cal calcula/ons can be performed in three different limits of field theory Fixed perturbation theory αs 0 Logarithmic resummation αs 0, αsl 2 fixed Kinematic expansion (parton shower) θij 0 Each expansion important in different regions

6 A simple example to understand the relevant physics is jet produc/on in e + e - collisions (LEP physics) Jet produc4on proceeds theore4cally through produc4on of partons 2 partons 3 partons θ 3 partons requires emission of extra gluon suppressed by power of α s But 3- parton cross sec4on becomes singular as θ 0 d d = s 2 +

7 A simple example to understand the relevant physics is jet produc/on in e + e - collisions (LEP physics) Remember: Partons are not observable, we need to deal with jets θj θ<θj 3 parton events with θ < θj are considered 2-jet events θj θ<θj To describe the inside of a jet, don t want expansion in α s Need kinema/c expansion

8 A simple example to understand the relevant physics is jet produc/on in e + e - collisions (LEP physics) Typically, jet cross- sec4ons can be described in fixed perturba/on theory d d = sf 0 ( )+ sf 2 1 ( )+ But large logarithms arise if two jets come close θ f 0 ( ) log 2 f 1 ( ) log3 2 Can only sensibly calculate using logarithmic resumma/on

9 For many processes of interest, all three different limi/ng calcula/ons are required Parton shower and hadronization are always required when realistic detector effects need to be taken into account

10 For many processes of interest, all three different limi/ng calcula/ons are required Higher fixed order corrections can have large effects

11 t,veto t,veto central t,veto For many processes of interest, all three different limi/ng The beam thrust spectrum for Higgs production for m H =165GeVattheTevatron the calcula/ons LHC for E cm are = 7 TeV required (right) The bands show the perturbative scale uncertainties as in section Higgs production (m H = 125 GeV), NNLO v NLL+NNLO NNLL+NNLO NLL +NLO NLL pp, 7 TeV m H /4 < µ R,F, Q < m H, 3 schemes MSTW2008 NNLO PDFs anti-k t, R=05 NNLO ε(p t,veto ) / ε central (p t,veto ) NLL+NNLO 1 1 cm the 09 LHC with E 09 cm = 7 TeV (right) The bands show important the perturbative in scale restricted uncertainties as in 08section regions of phase space p t,veto [GeV] p t,veto [GeV] gure 4: [GeV] T cut cm E cm NLL+NNLO = 196 TeV m H = 165 GeV σ(t cm cut ) [pb] 0 Higgs production cross section as a function of T cut E cm = 196 TeV Banfi, T cut Salam, Zanderighi ( 12) = 10 GeV NNLL+NNLO NLL +NLO NLL E cm = 7 TeV m H = 165 GeV [GeV] Comparison of cm cm fixed-order (NNLO) and matched resummed (NLL+NNLO) NNLL+NNLO ] 20 T cut cm Higher order resummation for m H =165GeVattheTevatron E cm = 7 TeV = 20 GeV T cut NNLL+NNLO

12 Goal of GENEVA is to go to first non- trivial order in both fixed order perturba4on theory and logarithmic resumma4on and combine with a parton shower

13 This talk describes our recent development of a new event generator called GENEVA What are we trying to do An illustra4ve example The GENEVA framework Results for e+e- event shapes Progress towards pp collisions

14 Thrust is the simplest variable to separate 2- jet events from mul/- jet events =1 T =1 max ~n X k ~n ~p k E cm τ 0: 2 pencil-like jets τ 1: > 2 jets τ<τ cut : Exactly 2 jets d d N LO : d d N NLO : 2( cut ) cut d incl 3 +

15 One can illustrate the interplay of fixed order and resummed calcula/ons using a simple illustra/ve example The inclusive cross sec4on can now be obtained as incl = 2 ( cut )+ Z d 3 incl ( > cut ) Perturba4ve expressions for exclusive 2- jet rate and inclusive 3- jet rate both contain large logarithms Lcut = Log(τcut) L = Log(τ) Form of these logarithms well known

16 The structure of the large logarithms follows a well known pavern Z incl = 2 ( cut )+ Z d 3 incl Z 2( cut ) 1+ s (L 2 cut + L cut + 1) + 2 s(l 4 cut + L 3 cut + L 2 cut + L cut + 1) + For exclusive 2- jet rate apple For inclusive 3- jet rate ( > cut ) d incl 3 s apple L ( ) s apple L 3 + L2 + L ( )+1 + LL resumma4on [all terms (α s L 2 cut) n ] needed if s L 2 cut 1

17 The structure of the large logarithms follows a well known pavern incl = 2 ( cut )+ Z d 3 incl ( > cut ) Some defini4ons I will use (1, ) : Sudakov Factor P ( ) d log (1, ) : Splidng func4on Conserva4on of probability (fundamental theorem of calculus) (1, cut )+ Z 1 cut P ( ) (1, ) =1

18 With this nota/on, can illustrate what other approaches are doing incl = 2 ( cut )+ Z d 3 incl ( > cut ) Combing LO with LL: Original CKKW prescrip4on Y apple apple 2( cut )= LO (1, cut ) Y apple d incl 3 = d 3 LO (1, ) Inclusive cross- sec4on gives Z 1 incl = LO (1, cut )+ d LO 3 cut Z 1 = LO (1, cut )+ LO = LO + O( s L cut ) cut P ( ) (1, ) (1, )+ Z 1 cut apple d LO 3 LO P ( ) (1, ) LO accuracy for both σ incl and dσ 3 incl

19 With this nota/on, can illustrate what other approaches are doing e Z e incl = 2 ( cut )+ Z apple d 3 incl e ( > cut ) Combining NLO with LL: Simple extension of CKKW Z e 2( cut )= NLO (1, cut ) d incl 3 = apple d NLO 3 + d 3 LO Z 1 0 P ( 0 ) (1, ) Inclusive cross- sec4on gives incl = NLO + O( 2 sl 3 cut) α s for α s L cut2 1 Large logarithms spoil NLO accuracy for σ incl

20 LL resumma4on not enough to merge different NLO calcula4ons Thus, while higher logarithmic resumma4on is important in its own right, also needed to combine NLO calcula4ons

21 Need to go to at least NLL (two orders more that LL) in resumma4on to be able to merge two NLO calcula4ons See also recent results from MINLO v20

22 This talk describes our recent development of a new event generator called GENEVA What are we trying to do An illustra4ve example The GENEVA framework Results for e+e- event shapes Progress towards pp collisions

23 First order of business is to separate perturba/ve expansions from kinema/c expansions Fixed perturbation theory Logarithmic resummation Kinematic expansion (parton shower) αs 0 αs 0, αsl 2 fixed θij 0 First two limits use expansion in α s (number of partons), while third does not Don t count number of partons, count number of jets Do calcula4ons for jet cross- sec4ons, and use shower to fill out jet

24 The main idea of Geneva is to make all internal objects physical jet cross sec/ons Calculate jet cross section + Assign cross section to parton event Use Parton Shower to fill jet Perturba4ve calcula4ons for events with limited # of jets, create 100 s of par4cles using shower

25 To obtain logarithmic resumma/on requires a fully factorizable jet defini/on A very convenient jet defini4on is called n- jedness [Stewart, Tackmann, Waalewijn] T N =2 X k min{ˆq 1 p k, ˆq 2 p k,, ˆq N p k } T N 0 : N pencil- like jets ˆq 1 T N Q : more than N jets ˆq 3 T N < T cut : Veto > N jets ˆq 2 Note that Τ 2 = τ Can easily be generalized for hadronic collisions

26 To obtain logarithmic resumma/on requires a fully factorizable jet defini/on A very convenient jet defini4on is called n- jedness [Stewart, Tackmann, Waalewijn] T N =2 X k min{ˆq 1 p k, ˆq 2 p k,, ˆq N p k } Factoriza4on theorem can be proven to all orders in perturba4on theory Allows for a systema4c method to resum logarithms at arbitrary order

27 This allows us to separate the total hadronic event into different jet mul/plici/es T 2 < T cut 2 T 2 > T cut 2 T 3 < T cut 3 T2 cut T3 cut T 2 > T cut 2 T 3 > T cut 3 T 4 < T cut 4 Calculate each jet cross sec4on to desired fixed order and resummed accuracy, and use shower to fill out jets with radia4on

28 The inclusive cross sec/on is given by summing over the different jet mul/plici/es For 2 different jet mul4plici4es can write d incl = d 2( cut ) 2 d 2 + d 3 incl ( 3 ) > cut d 3 d T 2 < T cut 2 T 2 > T cut 2 T 3 < T cut 3 Need expressions for both terms that are correct in both fixed and resummed perturba4on theory

29 apple How do we combine fixed order and resummed results? Z Z Fully differen4al fixed order result can be obtained using standard techniques d 2 ( cut Z ) = B 2 ( 2 )+V 2 ( 2 )+ d 2 Z d 3 B 3 ( 3 ) ( 3 ) < cut [ 2 2( 3 )] d incl 3 d 3 = B 3 ( 3 )+V 3 ( 3 )+ Z d 4 B 4 ( 4 ) ( 3 ( 4 ) 3) Most easily done with FKS subtrac4ons, which we choose in Geneva

30 How do we combine fixed order and resummed results? Z Fully differen4al resummed result can not be X Z obtained easily Expression that can be resummed is the 2- jedness apple d 2 ( cut ) d 2 distribu4on and cumulant d 3 d 2 = Z T T d 3 d 3 d 3 [ ( 3 ) )] [ 2 2( 3 )] Z Procedure to resum to arbitrary accuracy is known using SCET and results up to NNLL are available

31 How do we combine fixed order and resummed results? 2-jet d (T cut )= d resum (T cut )+ d 2 d 2 apple d FO d 2 (T cut ) d resum d 2 (T cut ) FO 3-jet ", d (T )= d FO d resum d resum d 3 d 3 d 2 dt d 2 dt FO # 4-jet d (T )= d LO d 4 d 4 Properly interpolates between fixed order result for large τ and resummed result for small τ

32 All this can be generalized and leads us to the master formula of GENEVA d incl d 2 d incl d 3 = d d 2 (T cut 2 )+ = d d 3 (T cut 3 )+ Z d 3 d 2 Z d 4 d 3 d d 3 (T 2 ) (T 2 > T cut 2 ) d d 3 (T 3 ) (T 3 > T cut 3 ) matching several jet multiplicities at NLO, with simultaneous resummation of N-jettiness for multiple N d incl d Nmax = d LO d Nmax where d = d incl d N+1 d N+1 apple d resum d N dt N d resum d N dt N FO If logarithms summed to appropriate order, gives correct inclusive cross- sec4on

33 As a valida/on, check that GENEVA reproduces correctly the thrust distribu/on at NLO and NNLL dσ/dt2 [nb/gev] LEP (912 GeV) NNLL +NLO 3 NLL +LO 3 NLL T 2 [GeV] dσ/dt2 [nb/gev] LEP (912 GeV) NNLL +NLO 3 NLL +LO 3 NLL T 2 [GeV] dσ/dt2 [nb/gev] LEP (912 GeV) NNLL +NLO 3 NLL +LO 3 NLL T 2 [GeV] analytic calculation of thrust distribution using the usual additive formula

34 As a valida/on, check that GENEVA reproduces correctly the thrust distribu/on at NLO and NNLL dσ/dt2 [nb/gev] LEP (912 GeV) NNLL +NLO 3 NLL +LO 3 NLL T 2 [GeV] dσ/dt2 [nb/gev] LEP (912 GeV) NNLL +NLO 3 NLL +LO 3 NLL T 2 [GeV] dσ/dt2 [nb/gev] LEP (912 GeV) NNLL +NLO 3 NLL +LO 3 NLL T 2 [GeV] analy4c calcula4on of thrust distribu4on using the usual addi4ve formula dσ/dt2 [nb/gev] LEP (912 GeV) GENEVA NNLL T +NLO 3 Partonic NNLL +NLO 3 NNLL NLO T 2 [GeV] dσ/dt2 [nb/gev] LEP (912 GeV) GENEVA NNLL T +NLO 3 Partonic NNLL +NLO 3 NNLL NLO T 2 [GeV] dσ/dt2 [nb/gev] LEP (912 GeV) GENEVA NNLL T +NLO 3 Partonic NNLL +NLO 3 NNLL NLO T 2 [GeV] GENEVA exactly reproduces analy4cal results

35 This solves the first of the problems posted at the beginning of talk Main problem: How do we calculate a cross- sec4on for events containing 100 s of par4cles? How do we calculate a cross- sec4on that is valid in all kinema4cal regions?

36 To match onto parton shower, need to fill jets with radia/on, without changing the thrust distribu/on we carefully worked out p 1 p 2 p 1 p 2 p 1 p 2 p 3 p 4 p 3 So far, we have assigned a weight to events that does two important things: Resums logs of the 2/3 jet resolu4on scale to NNLLʹ Has the 2 and 3 jet events calculated to NLO accuracy But our events s4ll only have 2, 3, or 4 partons need the parton shower to fill out our jets We will see the important effect of showering on other observables

37 To match onto parton shower, need to fill jets with radia/on, without changing the thrust distribu/on we carefully worked out p 1 1 p p 2 2 p p 1 1 p 2 2 Parton shower (Pythia8) p 1 p 2 p 1 p 2 p 3 3 p 3 p p 2 p 1 p 2 1 pp 4 4 p 3 p 1 p 2 Shower fills jets below T cut 2,3 but is forbidden to change underlying jet kinematics, in particular T How do we want to restrict Pythia s shower? We want to preserve the accuracy of our thrust distribu4on calcula4on p 4 p 3 Use the Pythia8 parton shower rou4ne, with modifica4ons We want 2/3 jet partonic events in GENEVA to shower into 2/3 jet events We want the 4 jet events to shower inclusively p 3 All this can be done using standard rou4nes in Pythia8 (UserHooks) However, hadroniza4on effects were not included in our resummed calcula4on, so use unconstrained Pythia8 model

38 To match onto parton shower, need to fill jets with radia/on, without changing the thrust distribu/on we carefully worked out dσ/dt2 [nb/gev] T 2 [GeV] LEP (912 GeV) GENEVA NNLL T +NLO 3 Showered (PYTHIA8) Partonic NNLL +NLO dσ/dt2 [nb/gev] LEP (912 GeV) GENEVA NNLL T +NLO 3 Showered (PYTHIA8) Partonic NNLL +NLO T 2 [GeV] T 2 [GeV] as adver4sed, showering does not change the thrust distribu4on dσ/dt2 [nb/gev] LEP (912 GeV) GENEVA NNLL T +NLO 3 Showered (PYTHIA8) Partonic NNLL +NLO 3 NLO dσ/dt2 [nb/gev] T 2 [GeV] ALEPH (912 GeV) OPAL (912 GeV) GENEVA+PYTHIA8 Default Tune 3 α s (m Z ) = 0118 No hadr dσ/dt2 [nb/gev] ALEPH (912 GeV) OPAL (912 GeV) GENEVA+PYTHIA8 Default Tune 3 α s (m Z ) = 0118 No hadr T 2 [GeV] dσ/dt2 [nb/gev] ALEPH (912 GeV) GENEVA+PYTHIA8 Default Tune 3 α s (m Z ) = 0118 No hadr T 2 [GeV] while hadroniza4on brings spectrum in agreement with data

39 This solves the first of the problems posted at the beginning of talk Main problem: How do we calculate a cross- sec4on for events containing 100 s of par4cles? How do we calculate a cross- sec4on that is valid in all kinema4cal regions?

40 This talk describes our recent development of a new event generator called GENEVA What are we trying to do An illustra4ve example The GENEVA framework Results for e+e- event shapes Progress towards pp collisions

41 Since we have a fully exclusive calcula/on, can make predic/ons for any other observable C-parameter Similar theoretically to thrust, but with power corrections, and nonperturbative effects Jet Broadening Very different observable, tests the ability of GENEVA to describe other observables with different log series GENEVA is making a prediction for these observables

42 C- parameter agrees very well with known higher log resumma/on, as well as LEP data dσ/dc [nb] LEP (912 GeV) GENEVA NNLL T +NLO 3 Showered (PYTHIA8) Partonic NNLL C +NLO 3 NLL C +LO C dσ/dc [nb] LEP (912 GeV) GENEVA NNLL T +NLO 3 Showered (PYTHIA8) Partonic NNLL C +NLO 3 NLL C +LO C dσ/dc [nb] 10 1 LEP (912 GeV) GENEVA NNLL T +NLO 3 Showered (PYTHIA8) Partonic NNLL C +NLO 3 NLO C 1 The parton shower does not significantly change the C spectrum Solid agreement between analytic NNLL, partonic GENEVA, and showered GENEVA

43 C- parameter agrees very well with known higher log resumma/on, as well as LEP data dσ/dc [nb] GENEVA+PYTHIA8 Default Tune 3 α s (m Z ) = 0118 No hadr ALEPH (912 GeV) OPAL (912 GeV) C dσ/dc [nb] C GENEVA+PYTHIA8 Default Tune 3 α s (m Z ) = 0118 No hadr ALEPH (912 GeV) OPAL (912 GeV) dσ/dc [nb] 10 1 ALEPH (912 GeV) GENEVA+PYTHIA8 Default Tune 3 α s (m Z ) = 0118 No hadr The default hadronization tune gives as good of an agreement as thrust C 1 MC/Data C parameter GENEVA+PYTHIA8 Default Tune 3 No hadr α s (m Z ) = C ALEPH (912 GeV) MC/Data thrust GENEVA+PYTHIA8 Default Tune 3 No hadr α s (m Z ) = 0118 ALEPH (912 GeV) T 2 [GeV]

44 Even Jet broadening, a very different observable is well described by GENEVA Becher, Bell dσ/db [nb] LEP (912 GeV) GENEVA NNLL T +NLO 3 Showered (PYTHIA8) Partonic NNLL B +LO 3 NLL B B dσ/db [nb] LEP (912 GeV) GENEVA NNLL T +NLO 3 Showered (PYTHIA8) Partonic NNLL B +LO 3 NLL B B dσ/db [nb] LEP (912 GeV) GENEVA NNLL T +NLO 3 Showered (PYTHIA8) Partonic NNLL B +LO 3 NLO B Pythia changes the spectrum from partonic GENEVA due to the lack of correlation with thrust favorable comparison to NNLL resummation for jet broadening SCETII : SCETI : d db = d d = s C F 2 s C F 2 8lnB 6 + B 4ln 3 + interesting to ask how accurately GENEVA is describing uncorrelated observables

45 Even Jet broadening, a very different observable is well described by GENEVA dσ/db [nb] ALEPH (912 GeV) OPAL (912 GeV) GENEVA+PYTHIA8 Default Tune 3 α s (m Z ) = 0118 No hadr B dσ/db [nb] ALEPH (912 GeV) OPAL (912 GeV) GENEVA+PYTHIA8 Default Tune 3 α s (m Z ) = 0118 No hadr B dσ/db [nb] ALEPH (912 GeV) GENEVA+PYTHIA8 Default Tune 3 α s (m Z ) = 0118 No hadr B good agreement with data through peak/early transition multijet corrections in the tail region MC/Data GENEVA+PYTHIA8 Default Tune 3 No hadr α s (m Z ) = 0118 ALEPH (912 GeV) B lack of correlation between τ and B means the N-jettiness multijet tail happens earlier for B

46 Even Jet broadening, a very different observable is well described by GENEVA dσ/db [nb] LEP (912 GeV) GENEVA NNLL T +NLO 3 Showered (PYTHIA8) Partonic NNLL B +LO 3 NLL B dσ/db [nb] GENEVA+PYTHIA8 Default Tune 3 α s (m Z ) = 0118 No hadr dσ/db [nb] B LEP (912 GeV) GENEVA NNLL T +NLO 3 Showered (PYTHIA8) Partonic NNLL B +LO 3 NLL B Showered agrees with analytic resummation, hadronized agrees with data dσ/db [nb] B ALEPH (912 GeV) OPAL (912 GeV) GENEVA+PYTHIA8 Default Tune 3 α s (m Z ) = 0118 No hadr B 25 ALEPH (912 GeV) OPAL (912 GeV) B GENEVA matches jet broadening resummation hadronization model correctly interpolates to data

47 This talk describes our recent development of a new event generator called GENEVA What are we trying to do An illustra4ve example The GENEVA framework Results for e+e- event shapes Progress towards pp collisions

48 For pp collisions, general framework remains unchanged, but several technical challenges need to be overcome Can use N-jettiness as in e + e - to distinguish jet multiplicities master formula: d incl d 0 = d d 0 (T cut 0 )+ Z d 1 d 0 d d 1 (T 0 ) (T 0 > T cut 0 ) The essential perturbative physics translates to pp collisions d (T0 cut )= d resum d 0 d 0 " d (T 0 )= d FO d 1 d 1 (T cut 0 )+ d resum d 0 dt 0, apple d FO (T0 cut ) d 0 # d resum d 0 dt 0 FO d resum d 0 (T cut 0 ) FO

49 For pp collisions, general framework remains unchanged, but several technical challenges need to be overcome Can use N-jettiness as in e + e - to distinguish jet multiplicities master formula: d incl d 0 = d d 0 (T cut 0 )+ Z d 1 d 0 d d 1 (T 0 ) (T 0 > T cut 0 ) Initial state radiation provides conceptual, technical challenges Resummation involves beam functions, sum over partonic channels FO calculations more challenging Requires matching GENEVA to an initial state parton shower pp collisions require multiple parton interaction (MPI) model

50 For pp collisions, general framework remains unchanged, but several technical challenges need to be overcome Can use N-jettiness as in e + e - to distinguish jet multiplicities master formula: d incl d 0 = d d 0 (T cut 0 )+ Z d 1 d 0 d d 1 (T 0 ) (T 0 > T cut 0 ) Initial state radiation provides conceptual, technical challenges Resummation involves beam functions, sum over partonic channels FO calculations more challenging Requires matching GENEVA to an initial state parton shower pp collisions require multiple parton interaction (MPI) model

51 Ini/al Drell- Yan plots show that the 200 combina/on of higher 40 order pp Z/ + (8 TeV) resumma/on and NLO calcula/ons work d /dt0 [pb/gev] d /dt0 [pb/gev] pp pp Z/ Z/ + (8 + TeV) (8 TeV) GENEVA GENEVA NNLL NNLL T +LO T +LO 1 1 Partonic Partonic NNLL+LO NNLL+LO 1 1 NNLL NNLL LO 1 LO T 0 [GeV] T 0 [GeV] (a) Peak Region agrees with resummation in the peak d /dt0 [pb/gev] d /dt0 [pb/gev] 1 1 partonic GENEVA, NNLL + NLO0 T 0 + [GeV] LO1 d /dt0 [pb/gev] pp pp Z/ Z/ + + (8 TeV) (8 TeV) GENEVA GENEVA NNLL NNLL T +LO T +LO 1 1 Partonic Partonic NNLL+LO NNLL+LO 1 1 NNLL NNLL LO LO 1 1 d /dt0 [pb/gev] pp Z/ + (8 TeV) GENEVA NNLL T +LO 1 Partonic NNLL+LO 1 NNLL LO T 0 [GeV] (b) Transition Region (a) 30 Peak Region d /dt0 [pb/gev] GENEVA NNLL T +LO 1 1 Partonic NNLL+LO 1 NNLL LO 1 d /dt0 [pb/gev] pp G T 0 [GeV (b) Transition R pp Z/ + (8 TeV) GENEVA NNLL T +LO 1 Partonic NNLL+LO 1 NNLL LO T 0 [GeV] (c) Tail Region agrees with FO Figure 14 TheGeneva partonic NNLL+LO 1 result is shown compared to the a of T 0 matched to fixed order at NNLL+LO 1 (a) peak, (b) transition, and ( shown for comparison is the pure resummedin result the at NNLL tailand the fixed-order order expansion of that resummation Compared to the e + e case, where contributing to the cross section is trivially proportional, in Drell-Yan the the PDFs requires treating every possible q q initial state separately, both 01 and the resummed cross sections In Geneva, the flavor sum is performed i sense, since every event has a definite flavor for the initial-state quarks and T 0 [GeV] T 0 [GeV] (c) Tail Region summed cross section is obtained after a sum over all events This means (c) Tail Region factors in eq (246) are evaluated for an individual flavor, and the entire exp Figure 14 TheGeneva partonic NNLL+LO 1 result is shown compared to theover analytic flavors resummation In the analytic resummation, since the matching between t Wednesday, Figure 14 TheGeneva partonic NNLL+LO 1 result is shown compared to the analytic resummation of April T matched 24, 13 to fixed order at NNLL+LO in the (a) peak, (b) transition, and fixed-order (c) tail regions crossalso sections is additive, there is instead only one way to per

52 We are very close to first LHC (V+jets, H+jets) implementa/on in GENEVA Improve resummation accuracy to NNLL Improve FO accuracy to NLO1 Add parton shower, hadronization, MPI Combine and test against DY studies at the LHC, Tevatron Add other processes

53 We are very close to first LHC (V+jets, H+jets) implementa/on in GENEVA Improve resummation accuracy to NNLL Improve FO accuracy to NLO1 Add parton shower, hadronization, MPI Combine and test against DY studies at the LHC, Tevatron Add other processes We are in the process of validating the combination NNLL + NLO0 + NLO1 + Pythia

54 In the past few weeks, we have managed to validate the addi/on of the Pythia shower for pp collisions dσ/dt0 [pb/gev] pp Z/γ l + l (8 TeV) GENEVA NNLL T +LO 1 Showered (PYTHIA8) T 0 [GeV] Partonic NNLL+LO 1 dσ/dt0 [pb/gev] pp Z/γ l + l (8 TeV) GENEVA NNLL T +LO 1 Showered (PYTHIA8) Partonic T 0 [GeV] NNLL+LO dσ/dt0 [pb/gev] pp Z/γ l + l (8 TeV) GENEVA NNLL T +LO 1 Showered (PYTHIA8) Partonic NNLL+LO T 0 [GeV] As before, adding Pythia8 showering does not change beam thrust dσ/dt0 [pb/gev] pp Z/γ l + l (8 TeV) GENEVA NNLL T +LO 1 Hadronized (PYTHIA8) Showered (PYTHIA8) Partonic dσ/dt0 [pb/gev] pp Z/γ l + l (8 TeV) GENEVA NNLL T +LO 1 Hadronized (PYTHIA8) Showered (PYTHIA8) Partonic T 0 [GeV] T 0 [GeV] Hadronization behaves as expected from field theory

55 Conclusions Geneva atempts to go to first non- trivial order in both fixed order and logarithmic expansion Going beyond LL resumma4on crucial to merge mul4ple NLO calcula4ons Results for e + e - are complete; results behave as expected and compare well against LEP results Results for pp are currently in valida4on stage Preliminary results look encouraging

56 Thank You!

57 Backup Slides

58 With this nota/on, can illustrate what other approaches are doing incl = 2 ( cut )+ Z d 3 incl Powheg prescrip4on Z ( > cut ) 2( cut )= NLO e (1, cut ) d incl 3 = NLO LO d LO 3 e (1, ) ep ( ) = 1 LO d LO 3 e Inclusive cross- sec4on gives incl = NLO e (1, cut )+ = NLO Z 1 cut NLO LO d incl 3 e (1, ) NLO accuracy for σ incl, LO accuracy for dσ 3 incl

59 With this nota/on, can illustrate what other approaches are doing incl = 2 ( cut )+ 2( cut )=e NLO e (1, cut ) Z d 3 incl MC@NLO prescrip4on d incl 3 = d 3 LO Z 1 e NLO = LO + V + LO Z Z P ( ) e Inclusive cross- sec4on gives Z Z 1 incl = e NLO (1, cut )+ Z cut 1 apple d = e NLO LO Z cut apple d = NLO LO 3 0 apple ( > cut ) LO P ( )+e e NLO P ( ) (1, ) NLO accuracy for σ incl, LO accuracy for dσ 3 incl 0 applee NLO P ( ) (1, )+ d 3 LO Z cut apple d LO LO P ( ) 3 LO P ( ) 0 LO P ( ) LO P ( )

60 With this nota/on, can illustrate what other approaches are doing incl = 2 ( cut )+ Z apple Z d 3 incl ( > cut ) Sherpa prescrip4on 2( cut )=e NLO (1, cut d ) incl apple 3 d NLO 3 = + d 3 LO apple Z 1 Z e e NLO = LO + V + LO P ( ) Z 1 incl MC@NLO = Z apple apple e Inclusive cross- sec4on gives cut + d 3 LO " d NLO Z 1 0 P ( 0 ) Large logarithms spoil NLO accuracy for σ incl Need very carefully defined P(τ) (higher log resumma4on) 0 d LO # (1, ) Z 1 e 0 P ( 0 ) (1, ) NLO LO P ( )

61 With this nota/on, can illustrate what other approaches are doing incl = 2 ( cut )+ Z apple Z d 3 incl ( > cut ) Sherpa prescrip4on 2( cut )=e NLO (1, cut d ) incl apple 3 d NLO 3 = + d 3 LO Z apple Z 1 Z e e NLO = LO + V + LO P ( ) Z 1 incl MC@NLO = Z cut + d 3 LO " apple apple e Inclusive cross- sec4on gives " d NLO Large logarithms spoil NLO accuracy for σ incl Need very carefully defined P(τ) (higher log resumma4on) 0 d LO # = O( 2 sl 3 cut) Z 1 0 P ( 0 ) (1, ) Z 1 e 0 P ( 0 ) (1, ) NLO LO P ( )

62 The structure of the large logarithms follows a well known pavern incl = 2 ( cut )+ Z d 3 incl ( > cut ) Nota/on for logarithmic accuracy 2( cut )= L 2 L 2 L 4 2 L 3 2 L 2 2 L 3 L 6 3 L 5 3 L 4 3 L 3 3 L 2 L

63 The structure of the large logarithms follows a well known pavern incl = 2 ( cut ) Z d 3 incl ( > cut ) Nota/on for logarithmic accuracy ( cut )= L 2 L 2 L 4 2 L 3 2 L 2 2 L 3 L 6 3 L 5 3 L 4 3 L 3 3 L 2 L LL 7

64 The structure of the large logarithms follows a well known pavern incl = 2 ( cut ) Z d 3 incl ( > cut ) Nota/on for logarithmic accuracy ( cut )= L 2 L 2 L 4 2 L 3 2 L 2 2 L 3 L 6 3 L 5 3 L 4 3 L 3 3 L 2 L NLL

65 The structure of the large logarithms follows a well known pavern incl = 2 ( cut )+ Z d 3 incl ( > cut ) Nota/on for logarithmic accuracy 2( cut )= L 2 L 2 L 4 2 L 3 2 L 2 2 L 3 L 6 3 L 5 3 L 4 3 L 3 3 L 2 L NLL

66 The structure of the large logarithms follows a well known pavern incl = 2 ( cut ) Z d 3 incl ( > cut ) Nota/on for logarithmic accuracy ( cut )= L 2 L 2 L 4 2 L 3 2 L 2 2 L 3 L 6 3 L 5 3 L 4 3 L 3 3 L 2 L NNLL